2018/06/21 by Vítor H. Fernandes, Manuel M. Jesus, Fernandes, V. H. +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #20M10 #20M20 #Chemical Synthesis and Analysis #FOS: Mathematics #Geometric and Algebraic Topology #Rings and Algebras (math.RA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1806.08440
openalex publication_date 2018/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce the notion of an orientation-preserving transformation on an arbitrary chain, as a natural extension for infinite chains of the well known concept for finite chains introduced in 1998 by McAlister \citeMcAlister:1998 and, independently, in 1999 by Catarino and Higgins \citeCatarino&Higgins:1999. We consider the monoid \mathscrPOP(X) of all orientation-preserving partial transformations on a finite or infinite chain X and its submonoids \mathscrOP(X) and \mathscrPOPJ(X) of all orientation-preserving full transformations and of all orientation-preserving partial permutations on X, respectively. The monoid \mathscrPO(X) of all order-preserving partial transformations on X and its injective counterpart \mathscrPOJ(X) are also considered. We study the regularity and give descriptions of the Green's relations of the monoids \mathscrPOP(X), \mathscrPO(X), \mathscrOP(X), \mathscrPOPJ(X) and \mathscrPOJ(X).